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====== Complex layer: Area mappings ======
After mapping edges, individual parts of the area can be marked in colour to enable a correlation between the graphic and the original image. To do this, CGRAPH maps individual points within the area, from which the area is filled. Such an assignment does not have to be unique; it depends on the function used.

Since areas are defined by internal points, this graphic requires that a border has already been mapped and that the image and original have been generated, either by [[circle_sections|circle segments]], [[straight_lines|line segments]] or [[polylines]].
 

The function is defined uniformly above the default values for all types of area mappings, because common mappings only make sense if the same function is used. The variable names z and param (as complex numbers) as well as x and y (as the real and imaginary parts of the variable z) are permitted.

CGRAPH provides several input options:

===== Input via default values =====

{{screen_EN:scr_area_mapping.png}}

Complex numbers can be entered in the **//Point in area//** field. After clicking on **//Add to list//**, they appear in the list on the right-hand side. Different colours are assigned to the individual points. These can be changed by double-clicking on an entry in the list.

===== Graphical input =====

By clicking on the **//Define areas in the original image//** button, CGRAPH switches to the Display tab and shows the original image and the image. Clicking on an area automatically colours the area and its image. If the area is ‘open’, i.e. has no boundaries, the entire accessible area is coloured. Above the original image is the **//Finish area selection//** button. After this, clicking on the original image will no longer lead to further definition of areas.

===== Editing points =====

Once an entry in the list on the right-hand side is selected, it can be edited.

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The value of the selected entry in the list is displayed on the left-hand side and can now be changed. Once you have finished making changes, click on **//Change values//**. If you want to leave the list entry unchanged, click on **//Cancel change//**.

An entry selected in the list can be removed by clicking on the **//Delete area//** button.

After clicking on the **//Create graph//** button, CGRAPH switches to the **//Graphics//** tab and shows the graph - the original image on the left and the image above the function on the right. 

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The example shows the image above the function f(z) = (1-z)/(2+z). The images used as examples for the graphic functions [[circle_sections|Circle segments]], [[straight_Lines|Line segments]] and [[Polylines]] were used as boundaries. The result corresponds to the symbol used for this graphic function.

The default values can be viewed in the tree on the left. If the function contains a parameter, it is displayed as a red square in the image. Double-clicking on this square allows you to change the parameter graphically by simply moving the mouse. Clicking in the image deactivates the parameter change. If you press the Shift key at the same time, the original parameter is restored. A more detailed explanation of this function can be found in the [[BedienungParameterC|notes on changing a complex parameter in the graphic display]]. 

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The specified points can be changed retrospectively – clicking on the **//list//** in the tree switches CGRAPH back to the tab with the specified points. The graphic is adjusted as soon as the **//Create graphic//** button is clicked.

[[Operating_the_Graphics|Notes on operating the graphic display]]

[[complex_plane|Back to overview]]